#265 ⟨a, b | ab=a, abb=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 7
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,abb=a ab - -
ab=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
68 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 934 | ⟨a, b | ab=a, abbb=a⟩ | φ(a) = a, φ(b) = b |
| 8 | 996 | ⟨a, b | ab=a, aab=aa⟩ | φ(a) = a, φ(b) = b |
| 8 | 1000 | ⟨a, b | ab=a, aba=aa⟩ | φ(a) = a, φ(b) = b |
| 8 | 1005 | ⟨a, b | ab=a, abb=ab⟩ | φ(a) = a, φ(b) = b |
| 8 | 1014 | ⟨a, b | ab=a, bab=ba⟩ | φ(a) = a, φ(b) = b |
| 9 | 2966 | ⟨a, b | ab=a, abbbb=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 3084 | ⟨a, b | ab=a, aabb=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 3092 | ⟨a, b | ab=a, abab=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 3096 | ⟨a, b | ab=a, abba=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 3101 | ⟨a, b | ab=a, abbb=ab⟩ | φ(a) = a, φ(b) = b |
| 9 | 3118 | ⟨a, b | ab=a, babb=ba⟩ | φ(a) = a, φ(b) = b |
| 9 | 3174 | ⟨a, b | ab=a, aba=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 8774 | ⟨a, b | ab=a, abbbbb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 9012 | ⟨a, b | ab=a, aabbb=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9028 | ⟨a, b | ab=a, ababb=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9036 | ⟨a, b | ab=a, abbab=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9040 | ⟨a, b | ab=a, abbba=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9045 | ⟨a, b | ab=a, abbbb=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9078 | ⟨a, b | ab=a, babbb=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9264 | ⟨a, b | ab=a, aaab=aaa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9272 | ⟨a, b | ab=a, aaba=aaa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9281 | ⟨a, b | ab=a, aabb=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9282 | ⟨a, b | ab=a, aabb=aba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9288 | ⟨a, b | ab=a, abaa=aaa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9297 | ⟨a, b | ab=a, abab=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9298 | ⟨a, b | ab=a, abab=aba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9305 | ⟨a, b | ab=a, abba=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9306 | ⟨a, b | ab=a, abba=aba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9315 | ⟨a, b | ab=a, abbb=abb⟩ | φ(a) = a, φ(b) = b |
| 10 | 9332 | ⟨a, b | ab=a, baab=baa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9340 | ⟨a, b | ab=a, baba=baa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9349 | ⟨a, b | ab=a, babb=bab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9366 | ⟨a, b | ab=a, bbab=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24458 | ⟨a, b | ab=a, abbbbbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24920 | ⟨a, b | ab=a, aabbbb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24952 | ⟨a, b | ab=a, ababbb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24968 | ⟨a, b | ab=a, abbabb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24976 | ⟨a, b | ab=a, abbbab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24980 | ⟨a, b | ab=a, abbbba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24985 | ⟨a, b | ab=a, abbbbb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25050 | ⟨a, b | ab=a, babbbb=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25428 | ⟨a, b | ab=a, aaabb=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25444 | ⟨a, b | ab=a, aabab=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25452 | ⟨a, b | ab=a, aabba=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25461 | ⟨a, b | ab=a, aabbb=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25462 | ⟨a, b | ab=a, aabbb=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25476 | ⟨a, b | ab=a, abaab=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25484 | ⟨a, b | ab=a, ababa=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25493 | ⟨a, b | ab=a, ababb=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25494 | ⟨a, b | ab=a, ababb=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25500 | ⟨a, b | ab=a, abbaa=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25509 | ⟨a, b | ab=a, abbab=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25510 | ⟨a, b | ab=a, abbab=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25517 | ⟨a, b | ab=a, abbba=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25518 | ⟨a, b | ab=a, abbba=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25527 | ⟨a, b | ab=a, abbbb=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25560 | ⟨a, b | ab=a, baabb=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25576 | ⟨a, b | ab=a, babab=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25584 | ⟨a, b | ab=a, babba=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25593 | ⟨a, b | ab=a, babbb=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25626 | ⟨a, b | ab=a, bbabb=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25794 | ⟨a, b | ab=a, aaba=aaab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25799 | ⟨a, b | ab=a, abaa=aaab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25800 | ⟨a, b | ab=a, abaa=aaba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25805 | ⟨a, b | ab=a, abab=aabb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25810 | ⟨a, b | ab=a, abba=aabb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25812 | ⟨a, b | ab=a, abba=abab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25846 | ⟨a, b | ab=a, baba=baab⟩ | φ(a) = a, φ(b) = b |